TSTP Solution File: SET102+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET102+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:05:40 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET102+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 02:40:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(member_type, type, (
% 0.13/0.41 member: ( $i * $i ) > $o)).
% 0.13/0.41 tff(unordered_pair_type, type, (
% 0.13/0.41 unordered_pair: ( $i * $i ) > $i)).
% 0.13/0.41 tff(singleton_type, type, (
% 0.13/0.41 singleton: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y_7_type, type, (
% 0.13/0.41 tptp_fun_Y_7: $i)).
% 0.13/0.41 tff(tptp_fun_X_8_type, type, (
% 0.13/0.41 tptp_fun_X_8: $i)).
% 0.13/0.41 tff(ordered_pair_type, type, (
% 0.13/0.41 ordered_pair: ( $i * $i ) > $i)).
% 0.13/0.41 tff(universal_class_type, type, (
% 0.13/0.41 universal_class: $i)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[X: $i, Y: $i] : refl((ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))) <=> (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))) <=> ![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y)))) <=> ![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(4,axiom,(![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','ordered_pair_defn')).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.41 tff(6,plain,(
% 0.13/0.41 ![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[5])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : (ordered_pair(X, Y) = unordered_pair(singleton(X), unordered_pair(X, singleton(Y))))) | (ordered_pair(X!8, Y!7) = unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (ordered_pair(X!8, Y!7) = unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))) = ordered_pair(X!8, Y!7)),
% 0.13/0.41 inference(symmetry,[status(thm)],[9])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), ordered_pair(X!8, Y!7))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[10])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (member(unordered_pair(X!8, singleton(Y!7)), ordered_pair(X!8, Y!7)) <=> member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.13/0.41 inference(symmetry,[status(thm)],[11])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 ((~member(unordered_pair(X!8, singleton(Y!7)), ordered_pair(X!8, Y!7))) <=> (~member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))) <=> (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(15,axiom,(~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unordered_pair_member_of_ordered_pair')).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (~![X: $i, Y: $i] : member(unordered_pair(X, singleton(Y)), ordered_pair(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.41 tff(23,plain,(
% 0.13/0.41 ~member(unordered_pair(X!8, singleton(Y!7)), ordered_pair(X!8, Y!7))),
% 0.13/0.41 inference(skolemize,[status(sab)],[22])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (~member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (^[U: $i, X: $i, Y: $i] : refl((member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))) <=> (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (^[U: $i, X: $i, Y: $i] : rewrite((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (^[U: $i, X: $i, Y: $i] : rewrite((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.41 tff(32,axiom,(![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','unordered_pair_defn')).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.13/0.41 tff(35,plain,(
% 0.13/0.41 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[34])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 ((member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> (~((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8))))))) <=> (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> (~((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8)))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[39])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> (~((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8)))))))) <=> ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[40, 38])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> (~((~member(unordered_pair(X!8, singleton(Y!7)), universal_class)) | (~((unordered_pair(X!8, singleton(Y!7)) = unordered_pair(X!8, singleton(Y!7))) | (unordered_pair(X!8, singleton(Y!7)) = singleton(X!8)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 ((~![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X))))))) | (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[43, 37])).
% 0.13/0.42 tff(45,plain,
% 0.13/0.42 (^[X: $i, Y: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(46,plain,
% 0.13/0.42 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.13/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.42 tff(47,plain,
% 0.13/0.42 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class) <=> ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(48,axiom,(![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','unordered_pair')).
% 0.13/0.42 tff(49,plain,
% 0.13/0.42 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.42 tff(50,plain,(
% 0.13/0.42 ![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.13/0.42 inference(skolemize,[status(sab)],[49])).
% 0.13/0.42 tff(51,plain,
% 0.13/0.42 (![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.13/0.42 tff(52,plain,
% 0.13/0.42 ((~![X: $i, Y: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(X!8, singleton(Y!7)), universal_class)),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(53,plain,
% 0.13/0.42 (member(unordered_pair(X!8, singleton(Y!7)), universal_class)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.13/0.42 tff(54,plain,
% 0.13/0.42 ((~(member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class))) | member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) | (~member(unordered_pair(X!8, singleton(Y!7)), universal_class))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(55,plain,
% 0.13/0.42 ((~(member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7)))) <=> member(unordered_pair(X!8, singleton(Y!7)), universal_class))) | member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.13/0.42 tff(56,plain,
% 0.13/0.42 (member(unordered_pair(X!8, singleton(Y!7)), unordered_pair(singleton(X!8), unordered_pair(X!8, singleton(Y!7))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[55, 44])).
% 0.13/0.42 tff(57,plain,
% 0.13/0.42 ($false),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[56, 24])).
% 0.13/0.42 % SZS output end Proof
%------------------------------------------------------------------------------